Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 31 of 50
The area of a parallelogram formed by two vectors \(\vec{A}\) and \(\vec{B}\) as its adjacent sides is equal to:
A
AB
B
\(AB \cos\theta\)
C
\(AB \sin\theta\)
D
\(AB \tan\theta\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \(AB \sin\theta\)
Concept:
Geometric interpretation of the magnitude of the vector cross product.

Formula:
$$\text{Area} = |\vec{A} \times \vec{B}| = AB \sin\theta$$

Solution:
The base of the parallelogram is \(A\). The height is the perpendicular component of vector \(\vec{B}\), which is given by \(B \sin\theta\).
$$\text{Area} = \text{base} \times \text{height} = A(B \sin\theta) = AB \sin\theta$$
This is exactly equal to the magnitude of the cross product of the two vectors.

Why other options are incorrect:
  • \(AB\) is the area of a rectangle with sides of length \(A\) and \(B\).
  • \(AB \cos\theta\) is the scalar dot product of the two vectors.
  • \(AB \tan\theta\) does not correspond to any standard geometric area for these vectors.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

Previous Question All Vectors & Equilibrium MCQs Next Question

Want to solve full-length papers under timed exam conditions?

Practice with zero-scroll lockdown sprints, dynamic latency zone timers, live peer selection telemetry, and the automated Amber mistake recovery loop.

Enter Arena Sprint iOS App Android App